Quasicrystals forming fractal patterns

I have read (sorry, I no longer have access to the source, which is the reason for the question (1) below) that one can find a fractal pattern if one
(a) shoots an electron through a two-dimensional plane perpendicular to a homogeneous magnetic field traversing a quasicrystal so that the magnetic field is one of certain irrational numbers with respect to the electric energies
(b) graphs the magnetic field versus the allowed energy levels of the electron.

I have several questions concerning this description:
(1) Do I have this description right?
(2) If so, how can one insure that a magnetic field/electric energy ratio is an irrational number if measurements are all rational?
(3) Since the fractal pattern requires a huge number of data points, wouldn't this also mean an impractical number of trials? [I am presuming a large number of trials rather than a single trial because of the twin requirements that the field be homogeneous and that one vary it in order to graph it. Is this an incorrect assumption?]